The first and last terms of an AP are a and l, respectively.
Question:

The first and last terms of an AP are a and l, respectively. Show that the sum of the nth term from the beginning and the nth term from the end is (a + 1).

 

Solution:
In the given AP, first term = a and last term = l.
Let the common difference be d.

Then, nth term from the beginning is given by
Tn = a + (n – 1)d             …(1)

Similarly, nth term from the end is given by
Tn = {l – (n – 1)d}            …(2)
Adding (1) and (2), we get:
a + (n – 1)+ {l – (n – 1)d}​
a + (n – 1)d + l – (n – 1)d
= a 
+ l 

                

​Hence, the sum of the nth term from the beginning and the nth term from the end is (a + l) .

 

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